Maths Mastery
https://www.harrodian.com/blog/category/maths-mastery
enMaths Mastery: The Power of Anchors
https://www.harrodian.com/blog/maths-mastery-power-anchors
<span class="field field--name-title field--type-string field--label-hidden">Maths Mastery: The Power of Anchors</span>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://www.harrodian.com/user/855" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Warren Rodricks</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Thu, 19/11/2020 - 10:14</span>
<div class="field field--name-field-blog-image field--type-image field--label-hidden field__item"> <img src="https://www.harrodian.com/sites/default/files/2020-11/Maths%20blog%20anchors/anchor.jpg" width="1344" height="1025" alt="Power of Anchors" typeof="foaf:Image" /></div>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><strong>Anchor tasks are key to ensuring that pupils of all abilities are engaged and inspired by Maths lessons. Warren Rodricks, explains why they work so well</strong></p>
<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span><span>Far and away the most common question parents ask me about mixed ability Maths teaching is this one: How do you ensure that every student, whatever his or her ability, is kept engaged and motivated whilst still making progress? If you share similar concerns about your child, let me reassure you. If teachers come to their lessons well planned and well prepared – invariably the case at Harrodian – the issue doesn’t arise. Enrichment is a required ingredient that is built into the fabric of every lesson in our classrooms, but not in the form of ‘extensions’ that take our pupils away from the year group curriculum. Instead, we encourage activities intended to take pupils' understanding deeper into the concept, however fast they’re picking it up, ensuring the gap between the attainment of different pupils is not widened. How do we do this? One of the key tools is our Anchor Task. </span></span></span></span></span></span></p>
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<p>Enrichment that takes pupils' understanding deeper into the concept is a required ingredient that is built into the fabric of every lesson</p>
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<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span><span>The Anchor Task opens the lesson. It is set up to give pupils a chance to explore the activity independently, as part of a partnership or in small groups. It requires dialogue between pupils and can tap into prior learning or the world beyond the classroom whilst stimulating and challenging children’s thinking. Good Anchor Tasks do this at various levels so all pupils of all abilities benefit. We call them ‘low-entry, high-ceiling’ activities. In essence, ‘low-entry’ means we want them to be easily accessible for all pupils to engage with. While ‘high ceiling’ means the task also offers numerous built-in opportunities to support further learning, as pupils become familiar with the idea. An example is set out below:</span></span></span></span></span></span></p>
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<h5><span lang="EN" xml:lang="EN" xml:lang="EN">Objective: Add 3-digit numbers</span></h5>
<ul><li><span lang="EN" xml:lang="EN" xml:lang="EN">Activity: Using post-it notes and the numbers 0-9, create 2 3-digit numbers when added together equals another 3-digit number</span></li>
<li><span lang="EN" xml:lang="EN" xml:lang="EN">The catch: You can only use each digit one time.</span></li>
<li><span lang="EN" xml:lang="EN" xml:lang="EN">The look: </span> <span lang="EN" xml:lang="EN" xml:lang="EN">⬜⬜⬜</span><span lang="EN" xml:lang="EN" xml:lang="EN">+</span></li>
</ul><p> <span lang="EN" xml:lang="EN" xml:lang="EN">⬜⬜⬜</span></p>
<p><span lang="EN" xml:lang="EN" xml:lang="EN">__________________________</span></p>
<p> = <span lang="EN" xml:lang="EN" xml:lang="EN">⬜⬜⬜</span></p>
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</tr></tbody></table><p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span><span>Let’s take apart the activity to examine how and why it works.</span></span></span><span lang="EN" xml:lang="EN" xml:lang="EN"><span><span> Top of our list of requirements for effective mixed ability teaching is collaboration. Dialogue – between teachers and pupils and, crucially, between pupils – plays a key role throughout the lesson. Tasks are built so that they prompt discussion that supports all pupils as they take part. Both for the explainers and for those receiving explanation, discussing maths one to one provides opportunities to develop understanding in every lesson. Setting out an idea so that someone else understands is challenging. Doing it helps higher attaining mathematicians gain a deeper insight into a concept. By the same token, those struggling with concepts in their own maths gain confidence from regular exposure to the language and processes of stronger mathematicians. Put simply, it’s a Win-Win.</span></span></span></span></span></span></p>
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<p>Top of our list of requirements is collaboration. Dialogue – between teachers and pupils and, crucially, between pupils – plays a key role throughout every lesson.</p>
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<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span>Next on our list of mixed ability essentials is ‘concrete’ apparatus. These physical props can often be a lot simpler than they sound. In this case, our tool consists of a collection of post-its. Simple as they are the Post its can make a big difference, providing a way to practise the skill of addition that pupils find more engaging and 'safer'. For one thing, if pupils make a mistake, it is not committed to paper and they can simply re-organise the post-its for a quick change to the sum. For another, the ‘playful’ atmosphere these simple props create encourages the sort of active participation from children that allows all pupils to take control of their learning. This makes the activity open to all and even allows pupils low in confidence to feel they can take risks safely. The added benefit of so-called ‘manipulatives’ is that they open up mathematical concepts, helping a learner to create meaning in a way they can physically feel at their fingertips.</span></span></span></span></span></p>
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<p>Physical props can make a big difference, providing ways to learn skills and to create meaning in a way that pupils can feel at their fingertips</p>
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<p><img alt="DSCN4451.JPG" data-entity-type="" data-entity-uuid="" src="https://www.harrodian.com/sites/default/files/2020-11/Maths%20blog%20anchors/DSCN4451.JPG" /></p>
<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span><span>The beauty of a good anchor task like this one is that it’s easy to build in activities that ‘stretch’ higher attaining learners. The original task as stated above, is to add two 3-digit numbers together to form another 3-digit number, without repeating any of the numbers used. The goal is to create as many number sentences as possible. As pupils succeed, we can add more complex challenges. One next step would be to ask learners to create the largest sum or the smallest sum possible with the post-it numbers and to explain how they know it is the largest or smallest sum. We can blend in knowledge of multiples by asking for an answer that is a multiple of 5 or 6. </span></span></span></span></span></span></p>
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<p>The beauty of a good anchor task is that it’s easy to build in activities that ‘stretch’ higher attaining learners</p>
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<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span><span>My favourite conclusion to this challenge is to ask the pupils to use two 3-digit numbers to make a 4-digit number starting with the number 2, whilst allowing them to repeat any number they wish, more than once even. The challenge then looks like this:</span></span></span></span></span></span></p>
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<h5><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span>Objective: Add 3-digit numbers</span></span></span></span></span></h5>
<ul><li><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span>Activity: Using post-it notes and the numbers 0-9, create 2 3-digit numbers when added together equals a 4-digit number with a 2 in the thousands column.</span></span></span></span></span></li>
<li><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span>The look: </span></span></span></span></span></li>
</ul><p><span><span><span> <span lang="EN" xml:lang="EN" xml:lang="EN"><span>⬜⬜⬜</span></span></span></span></span><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span>+</span></span></span></span></span></p>
<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span> ⬜⬜⬜</span></span></span></span></span></p>
<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span>____________________________</span></span></span></span></span></p>
<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span> = 2 </span></span><span lang="EN" xml:lang="EN" xml:lang="EN"><span>⬜⬜⬜</span></span></span></span></span></p>
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</tr></tbody></table><p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span><span>A pupil’s eyes will often light up when they hear that they can repeat any number they want to. The result is that there are usually a whole lot of 9s created. Which is great. The partners then work together to try and find an answer, spending time in discussion, experimentation and refinement, all of it creating deeper levels of understanding. And once in a while, a pupil will also show great number insight by stopping early in the task and telling me, ‘It can’t be done, Sir’ before launching into an explanation why not. (I’m leaving the reasons why for you to figure out here!)</span></span></span></span></span></span></p>
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<p>Every one of our pupils deserves both to be challenged and to be supported. The beauty of mastery and cleverly planned Anchor Tasks means this happens every lesson for each of them</p>
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<p><span><span><span><span lang="EN" xml:lang="EN" xml:lang="EN"><span><span>We believe every one of our pupils deserves both to be challenged and to be supported. The beauty of mastery and cleverly planned Anchor Tasks means this happens every lesson for each of them. We don’t ‘water-down’ the curriculum, or lower expectations. Instead, we provide the opportunity for all of our pupils to discuss the maths that’s on their minds and in the world around them...And more will follow on this last subject in my next blog.</span></span></span></span></span></span></p>
<p><img alt="059_Harrodian_19.jpg" data-entity-type="" data-entity-uuid="" src="https://www.harrodian.com/sites/default/files/Harrodian%20Images/Summertime%20images/059_Harrodian_19.jpg" /></p>
<p><em>Mr Rodricks welcomes feedback on this blog to <a href="mailto:website@harrodian.com">website@harrodian.com</a></em></p>
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Thu, 19 Nov 2020 10:14:46 +0000Warren Rodricks1467 at https://www.harrodian.comMaths Mastery: A Healthy Mix
https://www.harrodian.com/blog/maths-mastery-healthy-mix
<span class="field field--name-title field--type-string field--label-hidden">Maths Mastery: A Healthy Mix</span>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://www.harrodian.com/user/855" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Warren Rodricks</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Wed, 23/09/2020 - 09:14</span>
<div class="field field--name-field-blog-image field--type-image field--label-hidden field__item"> <img src="https://www.harrodian.com/sites/default/files/Harrodian%20Images/matt%27s%20pics%202019/Matt%27s%20pics%202019%20portrait/059_Harrodian_19.jpg" width="960" height="1440" alt="Warren Rodricks" typeof="foaf:Image" /></div>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><strong><span><span><span><span><span>In his first Maths Mastery Blog of the year, Warren Rodricks argues that the change to mixed ability Mathematics groups has had real benefits for all Lower Prep pupils </span></span></span></span></span></strong></p>
<p><br /><span><span><span><span><span>‘Change is the only constant in life,’ wrote the Greek philosopher Heraclitus more than 2500 years ago. As we come together as a school for the first time in what feels like a very long time, his words, still have an enduring relevance. In today’s ‘new normal’, it certainly feels that change will be a focal point of our lives for the foreseeable future. </span></span></span></span></span></p>
<p><span><span><span><span><span>This blog is about change of a rather specific kind that we are making to 8s and 9s Maths education at Harrodian, namely to teach those early years in mixed ability groups. Mixed ability teaching has always been a hotly debated topic so, as with all change, some will embrace it, others...not so much. So, what I plan to do with this blog and the next few is to set out why we think this change makes sense for Harrodian’s youngest learners. </span></span></span></span></span></p>
<p><span><span><span><span><span>One factor to bear in mind is the change that the pandemic has imposed on the school. As you know, to protect the students, we have created ‘bubbles’ at Harrodian and this has inevitably reduced the number of Maths groups we are running this year. This change has involved re-thinking our structures but it is not the most important factor in thinking about re-sculpting the experiences of our students. The theory and practice of Maths mastery has been much more important than our current 'bubbles' in driving the shift to Mixed Ability teaching.</span></span></span></span></span></p>
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<p>The theory and practice of Maths mastery has been much more important than our current 'bubbles' in driving the shift to Mixed Ability teaching.</p>
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<p><span><span><span><span><span>Our approach to mastery is influenced by two main schools of thought. One from Singapore, the other from Shanghai. One of the most interesting things about the development of mastery within these two systems is that they are both based on mixed ability classes. In fact, Singapore classrooms are usually made up of 40 students with only a single teacher and no teaching assistant. What’s more, Singapore teachers are generalists, not mathematical specialists. The question that rises then, is why does mastery work so well in this type of setting?</span></span></span></span></span></p>
<p><span><span><span><span><span>First and foremost is the concept of communication. Mastery asks students to talk to each other, to collaborate, to disagree, to explain. The need to communicate mathematically is an imperative for students to master a concept. Much of this time this type of communication comes naturally to the more confident and able students in a class. But, it is vital that every child takes part in these discussions both in a small group and as part the whole class. </span></span></span></span></span></p>
<p><span><span><span><span><span>Sometimes though, children lack the vocabulary and understanding required to initiate the discussion and this is part of why mixed groupings are so important. In these environments, children have their peers as role models and get to see first hand the way other students consider and process a concept. </span></span></span></span></span></p>
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<p>In Mixed Ability environments, children have their peers as role models and get to see first hand the way other students consider and process a concept.</p>
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<p><span><span><span><span><span>Some argue that this process only helps the weaker students as they gain from hearing mathematical dialogue which they would not necessarily hear in an ‘ability’ set. In fact, such conversations also benefit more able students as well. They are asked to explain their ideas and the concepts being studied and, through this, they gain a deeper understanding of the concept themselves. The logic is simple, being able to explain something so that someone else understands it requires a deep level of understanding in itself; it also means students often get to experience both being the ‘teacher’ and the ‘student’ with their peers and as a result their own understanding improves. Two heads are better than one is certainly true when developing a depth of understanding. </span></span></span></span></span></p>
<p><span><span><span><span><span>A second key to the success of mixed ability classes work is ‘pitch’. The pitch of all lessons is based on the required curriculum; it requires stronger mathematicians to keep on rising to the challenge, to keep on delving into their thought process in order to solve various problems. The wonderful thing about this is that those who struggle with Maths are being asked to do the same. </span></span></span></span></span></p>
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<p>Some students require more support than others, but they are all expected to work within the same curriculum band and to tussle with complex problems.</p>
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<p><span><span><span><span><span>One of the troubling aspects of differentiation (providing different work for different abilities) is that in the past it was used to ‘water-down’ curriculum expectations and in turn created greater distances between the most able and least able mathematicians in a class. Under mastery, the expectation is that all students will learn the core curriculum because it is what they deserve. High pitch, high expectations, high hopes. </span></span></span></span></span></p>
<p><span><span><span><span><span>The third piece in our mixed ability jigsaw is enrichment, sometimes known as ‘extension’. In the past, it was common to accelerate a student to the next year group’s curriculum as a way of challenging them. Mastery does not do this. Instead it enriches a student’s understanding by providing opportunities to deepen their understanding. When pupils finish their work quickly we don’t ask them to just wait quietly for others to finish. Instead we have enrichment activities which vary by topic and year group, but which always provide a new challenge for those who complete their work before their peers. </span></span></span></span></span></p>
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<p>When pupils finish their work quickly we don’t ask them to just wait quietly for others to finish. Instead we have enrichment activities which always provide a new challenge</p>
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<p><span><span><span><span><span>Looking back at the classes I have taught through my career it is clear to me that I have always needed to teach a range of abilities. Even in ability sets, what students know and understand still varies so we use the ideas set out here to ensure all students get the challenges they need. That’s why making the change to mixed ability groups with our younger pupils is something we welcome. The opportunity to create deeper dialogue for all of our students is the ultimate goal and one that will lead them to truly mastering their Mathematics.</span></span></span></span></span></p>
<p><em><span><span><span><span><span>Mr Rodricks welcomes feedback on this blog to <a href="mailto:website@harrodian.com">website@harrodian.com</a></span></span></span></span></span></em></p>
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Wed, 23 Sep 2020 08:14:33 +0000Warren Rodricks1443 at https://www.harrodian.comMaths Mastery: It's Good to Talk
https://www.harrodian.com/blog/maths-mastery-its-good-talk
<span class="field field--name-title field--type-string field--label-hidden">Maths Mastery: It's Good to Talk</span>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://www.harrodian.com/user/855" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Warren Rodricks</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Tue, 10/03/2020 - 14:55</span>
<div class="field field--name-field-blog-image field--type-image field--label-hidden field__item"> <img src="https://www.harrodian.com/sites/default/files/Harrodian%20Images/Maths%20blog/blur-button-classic-close-up-219570%20%281%29_0.jpg" width="1500" height="896" alt="Blurred Buttons" typeof="foaf:Image" /></div>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><span><span><strong><span><span><span>World Book Day reminds Mr Rodricks that Mathematics is a universal language that children need to speak frequently in daily life if they are to become fluent.</span></span></span></strong></span></span></p>
<p><span><span><span><span><span>As well as giving me the welcome opportunity to dress up in an inflatable rhino suit (<em>see bottom of page</em>), last week’s World Book Day also provided a timely reminder of how important it is to practise speaking the language of mathematics regularly. As part of the day, my 9s Maths class partnered up with Miss Horan’s PP3s to explore the mathematics underlying <em>James and the Giant Peach</em>. It was during this time that I was able to step back and watch how wonderfully well the students were using the language of mathematics to speak to each other. </span></span></span></span></span></p>
<p><span><span><span><span><span>Because Mathematics IS a language and, as with the more than 6500 languages that are spoken across the planet, mathematics is governed by numerous rules. Developing fluency often requires certain structures to be learnt and understood before they can be applied to more complex situations, successfully.</span></span></span></span></span></p>
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<p>Mathematics is a <em>lingua franca, </em>a global, even universal, language that transcends boundaries... but like any language, it has rules and nuances that can befuddle the early learner.</p>
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<p><span><span><span><span><span>In some senses, Mathematics is more than just another language. Even more than English, it is a <em>lingua franca, </em>a global, even universal, language that transcends almost all boundaries. In its use, there are rules or conventions that remain consistent. Take addition for example: 10 + 10 = 20. We may use different representations for the actual numbers and we may use different processes, but at its essence the core concept is shared across cultures and continents. Ten objects plus ten objects is going to equal 20 objects, no matter where we are. </span></span></span></span></span></p>
<p><span><span><span><span><span>Shape is the same. A square is a square, with exactly the same properties no matter what country you reside in. Whether it is in French, Spanish or Italian, a square has four vertices, four edges and four right angles. These are part of the features that make a square a square and it does not change between countries.</span></span></span></span></span></p>
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<p>Whether it is in French, Spanish or Italian, a square has four vertices, four edges and four right angles. These are the features that make a square a square</p>
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<p><span><span><span><span><span>This is not to say that this<em> lingua franca</em> is an easy language for all of us to master. The intricacies of a language are not always straightforward. To achieve fluency requires understanding rules of a complex and diverse nature and, like any language, mathematics has rules and nuances that can befuddle the early learner. Just because our students know some of the ‘words’ of mathematics, it does not make them fluent or mean they understand how the language works. </span></span></span></span></span></p>
<p><span><span><span><span><span>Making this distinction is often a source of disagreement between home and school. When a reception child is able to count to one hundred, a proud parent will often happily share this information as evidence of their child’s mathematical strength. A teacher will look at it with slightly more caution, knowing that while a child may speak some of the language, there may very well be gaps that still need addressing; that they may not understand what all the numbers mean or how they are built. </span></span></span></span></span></p>
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<p>Once we have mastered the basics of Maths ‘grammar and vocabulary’ we need to practise the spoken word. If we don’t do that we will never become fluent.</p>
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<p><span><span><span><span><span>Viewing Maths as a language can make it easier to understand how easily or quickly our students progress through it. Just as I am not a natural linguist, some are not natural mathematicians. I can learn to overcome my lack of natural ability though. And this is also the case for those who find Maths a struggle. As with languages, the key is establishing those key structures – the grammar and the vocabulary, if you like – as a foundation, at an early age. </span></span></span></span></span></p>
<p><span><span><span><span><span>Without such foundations, the basis of mathematics in a child is weak and destined to topple, at some point. But we need to be patient. We never rush through the curriculum: mastery tells us to build slowly and carefully, making sure the language really has been understood and learnt before moving on to the next challenge. </span></span></span></span></span></p>
<p><span><span><span><span><span>Once we have mastered the basics of Maths ‘grammar and vocabulary’ we need to practise the spoken word. Mastering any language means speaking it frequently and if we don’t do that we will never become fluent. Take my French for example. As a Canadian, I was required to learn that language but the teaching input was extremely limited in my early years of schooling and then much restricted even after primary school. You can imagine how fluent I ended up being, can’t you? Similarly, if our students only speak the language of Maths for 55 minutes a day, even though they do this each day for all of their school lives, they may well find themselves in the same boat.</span></span></span></span></span></p>
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<p>Weekends and holidays provide many moments when children can continue practising their vocabulary and developing their language as they interact with the world they live in</p>
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<p><span><span><span><span><span>To encourage fluency, we need to make the most of many opportunities we have to use the language of Maths beyond the classroom. One of my fondest memories of doing this involves my daughter learning to cook. Back then, the two of us would pretend we were hosting a cooking show. She would start the narration and I would happily jump in with questions that provided key details to our ‘viewers’. I was constantly talking about measurement – whether it was weight, volume, heat or time. Little by little, as she grew and took over the ‘show’, she began adding the language of measurement throughout her explanations. In turn, this learning acquired ‘by stealth’ and in ‘real-world’ play, fed back into a greater depth of understanding when she was back in the classroom.</span></span></span></span></span></p>
<p><span><span><span><span><span>This approach is vital to Maths Mastery thinking. As we see it, the application of skills and thoughts to the real world that bring an understanding of the world around us is,essentially, what all mathematics are for. It follows that evenings, weekends and holidays are not time off but provide many moments when children can continue practising their vocabulary and developing their language as they interact with the world they live in. </span></span></span></span></span></p>
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<p>We don’t want constant noise in the classroom, of course, but we know how important it is for our students to share their ideas, to disagree with each other and to talk through their process.</p>
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<p><span><span><span><span><span>That is also the reason why talking plays such a big part in our mastery programme at school. We don’t want constant noise in the classroom, of course, but we know how important it is for our students to share their ideas, to disagree with each other and to talk through their process. It is why we give our students time to speak to each other whilst solving problems, to engage in discussion in working through an answer and to reflect with one another after their work is completed. </span></span></span></span></span></p>
<p><span><span><span><span><span>Parents can play a huge part in all of this. The home-school partnership – based on casual communication rather than formal practice – plays a key role in our children becoming stronger mathematicians. Speaking to your child on the school run, as you make dinner or while watching your beloved football team can provide opportunities for him or her to see Maths working outside the classroom in ways which, thanks to their context, can be especially significant and memorable.</span></span></span></span></span></p>
<p><span><span><span><span><span>Watching my 9s discuss, explain and question the Pre-Prep children on World Book Day reminded me a lot of what we try to do as teachers for them. And observing how the PP3s used their own grasp of Maths to respond reminded me how well the learning process works when it is a conversation. By sharing and learning to love the language of mathematics and having fun with it, our students give themselves the best chance of truly mastering it. </span></span></span></span></span></p>
<p><img alt="Prep%20Team%20-%20Jungle%20Book.jpg" data-entity-type="" data-entity-uuid="" src="https://www.harrodian.com/sites/default/files/Harrodian%20Images/English/World%20Book%20Day%202020/Prep%20Team%20-%20Jungle%20Book.jpg" /></p>
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<p>By sharing and learning to love the language of mathematics and having fun with it, our students give themselves the best chance of truly mastering it. </p>
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Tue, 10 Mar 2020 14:55:36 +0000Warren Rodricks1337 at https://www.harrodian.comMaths Mastery Blog: How Can I Help?
https://www.harrodian.com/blog/maths-mastery-blog-how-can-i-help
<span class="field field--name-title field--type-string field--label-hidden">Maths Mastery Blog: How Can I Help?</span>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://www.harrodian.com/user/855" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Warren Rodricks</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Thu, 16/01/2020 - 12:01</span>
<div class="field field--name-field-blog-image field--type-image field--label-hidden field__item"> <img src="https://www.harrodian.com/sites/default/files/blog/2020-01/060_Harrodian_19.jpg" width="954" height="769" alt="Warren Rodricks helps a pupil" typeof="foaf:Image" /></div>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><strong><span><span><span>How do you help your child with her homework without causing confusion or an argument. Warren Rodricks offers his four rules for frustration-free Maths home studies</span></span></span></strong></p>
<p><span><span><span>One of the questions parents ask me most often is 'How can I help my child with their Maths?'. Back when I was starting out on the Maths Mastery path years ago the answer seemed to me to be relatively straightforward. Start by trying to look at the world and specifically, mathematics, through the child’s eyes. Sit down with him or her over their homework and let them lead the process and ask questions as needed. </span></span></span></p>
<p><span><span><span>Some years on, experience has taught me the teaching ideal I had prescribed isn’t quite as simple to achieve as I had imagined. Then I had no children of my own. Today, as a father myself, I've learnt from personal experience about the unique frustrations that teaching your own child brings with it. </span></span></span></p>
<p><span><span><span>As much as I adore her, I have to admit that no pupil I have encountered in many years of teaching has challenged my skills and my patience more than my own daughter. It’s not that she’s difficult. Quite the opposite: thoughtful, reflective, empathetic and hard-working, Olivia is a model student. Even so, despite our closeness, when explaining how to tackle a problem I’ve often found myself caught up in conflict. 'That’s not what Miss said' or 'That’s not how Miss does it', have been common phrases in exchanges that have sometimes turned into battles. </span></span></span></p>
<p><span><span><span>I know from talking to parents that many of them have encountered similar clashes. It’s often a question of divided loyalties. Like my daughter, every pupil wants to get his or her Maths right. But just who is right? Facing a choice between following their beloved parent or their trusted teacher it’s hardly surprising that children are left feeling anxious, confused or angry.</span></span></span></p>
<p><span><span><span>So how can we defuse this conflict before it happens and help our children along the way? As both a parent and a teacher, I have learnt four things, down the years, all of them derived from Maths Mastery that I think can make a difference. I’ll refer to them as rules, but really they are more like suggestions, really, really good ones.</span></span></span></p>
<p><span><span><span><strong>Rule 1: It is not about how we see the world, it is about how they see the world.</strong></span></span></span></p>
<p><span><span><span>This first rule is the Maths Mastery principle I outlined in the first paragraph of this blog. You begin by asking your child to explain to you what they know. As I have already confessed this first rule was one I found easier to promote back in the days before I was a Dad. What makes it so difficult to stick to is that as parents we don’t want our children to struggle. We just want them to ‘get it’ and we constantly find ourselves wanting to provide solutions.</span></span></span></p>
<p><span><span><span>Hard as it is, though, I try to resist the temptation to lead the way. Struggle is essential to development and by jumping to the rescue too early I deny my daughter the opportunity to develop her <strong>metacognition* (see below)</strong>. One of the aspects I love about mastery is the approach to a concept. Before I do anything, I ask the students to show me or tell me what they already know. I let my students think, contemplate, discuss, debate before I say anything. </span></span></span></p>
<p><span><span><span>However, with my daughter I struggle with this even to this day. As the years have passed, I have become much more aware of this and now I try to start our discussions with something like, “What do you think needs to be done?” or “How would you do it?” They are questions that place the responsibility on my daughter and allow her to show me what she is doing in school and how she is making sense of it. At this point and during most points, to be honest, it doesn’t matter what I know, it only matters what she knows. I can offer tweaks to her method but I don’t try to sell her on my method. Because that is just it. It’s my method. What works for me won’t necessarily work for her.</span></span></span></p>
<p><span><span><span><strong>Rule 2: Use what you have around you to help make learning concrete.</strong></span></span></span></p>
<p><span><span><span>At times, mathematics has been rushed for many students and they are asked to think in the abstract before having a concrete understanding of a concept. The concrete understanding of a number or a concept is vital when trying to build towards higher level understanding. The beauty of early years teaching is that it consistently places the concrete world directly into the hands of children and asks them to construct meaning for themselves. Somewhere, for some strange reason, schools across the world lose sight of this. This wonderful way of learning is replaced by abstraction and that hands-on experience can no longer be drawn upon for a student to understand what is happening.</span></span></span></p>
<p><span><span><span> At school, we have a plethora of tools to help us. From counters, to number fans, to multilink blocks. What these resources do is place learning back into the hands of our students. They allow students to create, make mistakes and then re-create. At home, many, if not most students, would benefit from the same type of resources. Luckily you don’t have to rush out and buy a heap of manipulatives because the household is already full of useful tools. Dried pasta is a great counter that students can add, subtract, multiply and divide with. Any cake, chocolate bar, pie or pizza (my personal favorite) can be used in the exploration of fractions. This concrete approach is used throughout our time at school and it is an excellent way of linking up what we do here with the support they may need at home. </span></span></span></p>
<p><span><span><span><strong>Rule 3: Use the ‘real’ world as a way to support understanding but also as a way to extend learning. </strong></span></span></span></p>
<p><span><span><span>Mathematics is not a language to be spoken only in classrooms and used only as part of theories. It is meant to help us understand the wonderful world around us. As such, the best way to help students who may struggle with a concept or students who need an extra challenge is to use the outside world to further their development. One of the methods I use as a teacher is to ask my students where they see a concept or calculation in the world and then to write a realistic story about it. It forces them to think about how we use the mathematics outside of the classroom and what is real or unreal given the numbers or concepts involved. This in turn gives them a deeper understanding of why the maths is important and how it actually works beyond our lessons. It is something that I use with my daughter at home. </span></span></span></p>
<p><span><span><span>By asking our children to connect their learning to their surroundings we give them both structures needed to understand as well as open them up to possibilities of why mathematics makes a difference and this can be huge in them developing a positive attitude towards a subject that many find challenging.</span></span></span></p>
<p><span><span><span><strong>Rule Four: Time is important but it is a case of quality over quantity.</strong></span></span></span></p>
<p><span><span><span>I have lived a fair few years and worked at being a few different things and never have I ever had a mathematical emergency. No one has ever jumped out from behind a bush demanding the answer to 6 times 5. Thus, as you work with your child at home, afford them the time to think, to rethink and to reflect. It does them much better thinking through one question properly during their ten-minute maths than racing through all of them making errors throughout. Time does become important and consolidation requires a certain quantity of questions to be answered accurately, but to best support them at home, give them the luxury of the time you have to make sure they don’t become anxious when finding a concept challenging. What have these lessons meant to me? Well, my daughter still feels comfortable asking me for help. Despite the occasional burst of emotion (mainly mine) she knows I want to help and she knows I won’t impose my understanding on her. She is happy to let me know when she does not quite get something and she knows we’ll work as a partnership to help her figure things out. However, I know she also needs to figure out the mathematical world that she is encountering with greater independence and no amount of my knowledge will help, at times. Which is a lot like the rest of a child’s growth; we may have been there and done that, but now it’s their turn to figure things out.</span></span></span></p>
<p><strong>*Metacognition</strong> is central to Maths Mastery. It involves asking students to consider their own thinking, to ask what and why they are doing the things that they do. For more detail please see <a data-entity-type="node" data-entity-uuid="eeebc43c-b95b-4a29-8ca6-3496a4a4147e" href="https://www.harrodian.com/blog/maths-mastery-same-samebut-different" title="Maths Mastery blog">my last post</a>.</p>
<p>Mr Rodricks welcomes feedback on this blog to <a href="mailto:website@harrodian.com">website@harrodian.com</a></p></div>
Thu, 16 Jan 2020 12:01:04 +0000Warren Rodricks1291 at https://www.harrodian.comMaths Mastery: Same-Same...but Different
https://www.harrodian.com/blog/maths-mastery-same-samebut-different
<span class="field field--name-title field--type-string field--label-hidden">Maths Mastery: Same-Same...but Different</span>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://www.harrodian.com/user/855" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Warren Rodricks</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Fri, 29/11/2019 - 08:21</span>
<div class="field field--name-field-blog-image field--type-image field--label-hidden field__item"> <img src="https://www.harrodian.com/sites/default/files/Harrodian%20Images/Maths%20blog/neon-signage-2681319.jpg" width="1401" height="1080" alt="Think about things differently" typeof="foaf:Image" /></div>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><span><span><span><span><span>Since I returned to England, after some years working in Thailand, the cultural influence has lingered on in various ways. I still love the spices and the beaches but it’s the people and their outlook on life that are truly unforgettable. Two phrases encapsulate the essence of Thai culture for me. ‘<em>Jai yen yen’</em> equates to a cool heart or in other words, remaining calm. <em>‘Mai pen rai’ </em>means no worries. They’re both in my mind, inspiring me as I work. Teaching children provides a wonderful unpredictability to the day, as children see the world in amazingly different ways. But as a teacher it’s also vital to remain calm and not to worry about everything. Be calm, don’t worry. Essential starting points! </span></span></span></span></span></p>
<p><span><span><span><span><span>It’s a third phrase that I learnt in Thailand that is the focus of this blog. It is a phrase spoken in English and not in Thai. </span></span></span></span></span></p>
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<p>'Same-same but different', is a Thai phrase (but spoken in English) used to describe things that are similar, yet not exactly so.</p>
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<p><span><span><span><span><span>It is often heard in markets as part of the negotiation process. If an item you want is not available for one reason or another, you may be offered a something similar, something close to what you wanted, but not identical. Same-same...but different. </span></span></span></span></span></p>
<p><span><span><span><span><span>So then, what does this phrase have to do with a mastery blog? I am fortunate enough to be working with an incredible team of Maths teachers. Each of them is dedicated, knowledgeable and caring but each is, inevitably, also a unique individual shaped by diverse experience into his or her own particular ways of seeing the world and teaching children. It seems to me bizarre to ask any one of us to try and teach the way another does. Yet, in schools across the country, this type of ‘equality of opportunity’ is regarded as desirable. </span></span></span></span></span></p>
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<p>It seems to me bizarre to ask any one of us to try and teach the way another does. Yet, in schools across the country, this is regarded as desirable. </p>
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<p><span><span><span><span><span>The notion first began as part of the new national curriculum. The idea that a child could move from one place of the country to another without missing a beat in terms of their lessons was viewed as advantageous. There is a logic to this. The national curriculum meant that children could not be disadvantaged by location or in the skills they were taught because there was a basic requirement that all teachers and schools had to meet. In this instance same-same is good. </span></span></span></span></span></p>
<p><span><span><span><span><span>But what was lost in this proposal was the knowledge that children are inherently different and have different needs, not just from county to county but from class to class. Equally, teachers bring with them different experiences and different strengths, which they apply to their classes in an effort to inspire. Both state and independent schools have often attempted to get teachers planning together so that the teaching sequence was similar if not identical and, under such organisation, it became easier for teachers to plan. Easier for teachers to resource. Easier for schools to monitor. But as I see it, in this instance, ‘easy’ is not in the best interest of the pupils. The beauty of a child and his or her mind is that they are each unique, one of a kind. We cannot teach in 22 different ways in a class of 22, it’s true but we can consider the differences in our students and in our own styles. In this case, then, same-same is not good. </span></span></span></span></span></p>
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<p>The beauty of a child and his or her mind is that they are each unique, one of a kind. </p>
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<p><span><span><span><span><span>Mastery adds an important extra layer to what is already a rather tumultuous landscape. At Harrodian, mastery brings with it a very important aspect of ‘sameness’ but also with a difference. We want our students to take the same national curriculum that all pupils do, but we want them to view the subject and the curriculum through the Mastery lens. That means learning and experiencing Mathematics through five key shared learning methods which we use in our lessons. These five pillars of mastery are set below with a little more explanation which I hope may clarify what I’m getting at.</span></span></span></span></span></p>
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<p>Mastery means learning and experiencing Mathematics through five key shared learning methods which we use in our lessons, though not all five will necessarily be used in a single lesson. </p>
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<ol><li><span><span><span><span><span><strong><span><span>Metacognition: </span></span></strong><span><span>this involves asking the students to think about their own thinking, which is essentially reflecting upon what and why they are doing the things that they do. This reflection allows a student to carefully consider the process they are studying and why they are making the decisions they are in trying to find an answer. This becomes key in applying skills to new contexts. Equally important is how metacognition helps students identify possible limitations and build their own ideas on where they need further development, which is a significant skill for all.</span></span></span></span></span></span></span></li>
<li><span><span><span><span><span><strong><span><span>Visualisation</span></span></strong><span><span> is a two-fold concept within mastery. First, it involves the movement from concrete objects to picture representation and model-making. In doing so, a deeper level of understanding can be gained which is the precursor for students working with abstractions in their lessons. Abstractions flood everyday mathematics lessons; for the most part we do not even think about abstractions as abstractions (a digit form of a number is an abstraction as it represents a quantity, for example). The second aspect of visualisation involves using real-world examples so that students can ‘see’ the Maths around them and the impact it has. If you remember the problem with the tea I highlighted in my last blog, you will know it is vital that problems are rooted in reality so our students can make connections that deepen their understanding. </span></span></span></span></span></span></span></li>
<li><span><span><span><span><span><strong><span><span>Generalisation: </span></span></strong><span><span>generalising involves taking a specific example and building a rule based on what pupils uncover. In doing so, they are able to test their rule with other specific examples leading to greater understanding of how the rule is applied and what exceptions to the rule may look like. The idea is that students start to uncover the rules of mathematics themselves, working to prove their own theories correct.</span></span></span></span></span></span></span></li>
<li><span><span><span><span><span><strong><span><span>Number sense: </span></span></strong><span><span>Traditional notions of mathematics have often viewed number as static, as fixed. But within mastery, number is viewed as fluid flexible and that the meaning assigned to a number requires significant reasoning. A number’s value can ‘depend’ on context. Is it a little? Is it a lot? Well, it depends on the details surrounding the use of the number. Strong number sense allows students to see the possibilities and impossibilities of a question before they even need to calculate. It also allows them to spot errors on their own after they have completed tasks.</span></span></span></span></span></span></span></li>
<li><span><span><span><span><span><strong><span><span>Communication:</span></span></strong><span><span> Finally, communication involves our students discussing, disagreeing and developing ideas with each other. Our students are given frequent opportunities to analyse and synthesize in an effort for them to deepen their understanding through their own explanations whilst extending their learning by listening to their peers. The ‘give and take’ in a conversation between partners is a powerful learning process and amongst peers it tends to spiral both participants to greater levels of understanding. </span></span></span></span></span></span></span></li>
</ol><p><span><span><span><span><span>It's important to point out that we would not expect all five ingredients to be included in a single lesson. Depending on student needs, a teacher may spend longer in one area than another. </span></span></span></span></span></p>
<p><span><span><span><span><span>But, as a group of lessons unfold, we will have provided the opportunity for all of our students to experience each of the key concepts. The way this looks will vary from class to class but I hope you will agree that this is both a good thing and an absolutely necessity for student development. </span></span></span></span></span></p>
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<p>Same-same but different, as it applies in a mathematical context, is all about balance. Sometimes, a very delicate balance.</p>
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<p><span><span><span><span><span>For me the idea of Same-same but different, as it applies in a mathematical context, is all about balance. Sometimes, a very delicate balance. I believe the ideal learning environment is a place where teachers view mathematics in a similar way, where high standards and the ability to add flair and excitement to lessons are valued, and where teachers can draw on personal experience in order to enrich lessons and enlighten students. I am happy to say this is just the context we are creating within Lower Prep mathematics at Harrodian. I’m confident it will lead to our students loving Maths as well as reaching their full potential.</span></span></span></span></span><br /><br />
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Fri, 29 Nov 2019 08:21:38 +0000Warren Rodricks1263 at https://www.harrodian.comMaths Mastery: The Problem with Problems
https://www.harrodian.com/blog/maths-mastery-problem-problems
<span class="field field--name-title field--type-string field--label-hidden">Maths Mastery: The Problem with Problems</span>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://www.harrodian.com/user/855" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Warren Rodricks</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Mon, 14/10/2019 - 15:11</span>
<div class="field field--name-field-blog-image field--type-image field--label-hidden field__item"> <img src="https://www.harrodian.com/sites/default/files/Harrodian%20Images/Maths%20blog/tea-2179175_1920.jpg" width="1500" height="983" alt="Eleven cups of tea" typeof="foaf:Image" /></div>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><span><span><strong><span><span><span>In his latest blog, Warren Rodricks explains how eleven cups of tea changed the way he thinks about mathematical ‘word problems’ </span></span></span></strong></span></span></p>
<p><span><span><span><span><span>I can remember the moment back in my early days as a teacher when I started rethinking the value of Maths ‘problems’ in earnest. The conversation, which took place at the end of what, I thought had been quite a good lesson, went like this:</span></span></span></span></span></p>
<p><span><span><span><span><span>“Well done, class. Not an easy problem to solve, but you worked really well.”</span></span></span></span></span></p>
<p><span><span><span><span><span>“But Mr Rodricks.” A tiny voice piped up behind me.</span></span></span></span></span></p>
<p><span><span><span><span><span>“Yes?” I replied.</span></span></span></span></span></p>
<p><span><span><span><span><span>“Do you actually drink 11 cups of tea?”</span></span></span></span></span></p>
<p><span><span><span><span><span>“Umm, well, no, I don’t...actually...good point,” I muttered, feeling somewhat taken aback as I looked around the disappointed faces across the room. </span></span></span></span></span></p>
<p><span><span><span><span><span>I do drink tea. Long before I arrived in the UK I liked it and still do. Quite a bit. I especially enjoy my first cup when I get to school. It eases me into the day ahead. I also thoroughly enjoy a cup in the evening; after dinner, sat at home with various members of the Rodricks household. But that is it, really. Two cups. Never, in my life, have I had 11 cups of tea in a day. Actually, I don’t believe I’ve ever had 11 cups of anything in a day. Which brought me to the heart of the problem with what I will call the ‘Eleven Cuppas’ problem. It just didn’t ring true. And why bother to solve a problem when it’s not <em>really </em>a problem worth solving? </span></span></span></span></span></p>
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<p>The ‘Eleven Cuppas’ problem just didn’t ring true. And why bother to solve a problem when it’s not <em>really </em>a problem worth solving?</p>
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<p><span><span><span><span><span>Growing up, I can remember all sorts of word problems like the ‘Eleven Cuppas’ one above: problems that existed solely within the contrived context of a maths class. Whether the subject in question was cats, cars or cookies, the problems hid calculation in word form. There were multiple elements to the questions and I recall having to sift through plenty of information to find the data I needed. But the problems lacked plausibility. Sure, they might have helped develop mathematical reasoning and thinking but they missed the chance to take these skills to a deeper level. In those days, it wouldn’t really have mattered to the teachers that they didn’t actually drink 11 cups of tea a day. Students learnt to extract information from the question without really thinking about what it meant. Within mastery, I am happy to say, this is changing. </span></span></span></span></span></p>
<p><span><span><span><span><span>The point about ‘Eleven Cuppas’ is that it doesn’t emerge from true experience. The fact that my students quickly cottoned onto this showed that the maths was ‘only’ theoretical. Yes, we could solve the problem and discuss it in detail, but only in a way that confined it to an abstract space within the walls of the classroom that seemed unconnected and irrelevant to real life.</span></span></span></span></span></p>
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<p>We could solve the problem and discuss it in detail, but only in a way that confined it to an abstract space within the walls of the classroom that seemed unconnected and irrelevant to real life.</p>
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<p><span><span><span><span><span>So, what is a good problem? Let me give you an example: </span></span></span></span></span></p>
<hr /><p><span><span><strong><span><span><span>The Birthday Present</span></span></span></strong></span></span></p>
<p><span><span><em><span><span><span>Mr Rodricks is a very lucky father. Olivia, his daughter, is a remarkable little girl. Though really, she is not so little any more. As she is growing up, she is getting to be more expensive. Her tastes are changing and she does enjoy the odd purchase here and there. However, her latest possible expenditure is not for her. You see, she has decided, along with a couple of her friends, to put some money together to buy another one of their other friends a birthday gift. They have decided to buy a £321 smart watch. Now, Mr Rodricks can appreciate their kindness and he is certainly a BIG fan of watches. But this seems a lot to him. To which Olivia argues, “But I’m not paying all of it. We are going to share the cost.” </span></span></span></em></span></span></p>
<p><span><span><em><span><span><span>Given this, how much will Olivia have to pay?</span></span></span></em></span></span></p>
<p>The first crucial difference in the Birthday Present problem is that it’s up to the students to choose how they are going to solve the calculation. The lesson starts with the problem rather than how to divide or different methods of division, asking students to show us what they understand and what skills they already possess. Planning lessons this way means that as teachers we aren’t teaching pupils what they already know. Instead, we can focus on choosing the most suitable method for the purpose (‘calculation flexibility’) and handle any misconceptions as they arise. <span><span><span><span><span>The story above is filled with context. Real world and real, mathematical context. Students develop a sense of how mathematics plays a part in their decision making, even if they are not specifically thinking about the maths. They also have to think about the relationships at play and the mathematical consequences that emerge from them. </span></span></span></span></span></p>
<p><span><span><span><span><span>Obviously, the calculation is important – we want our students to be accurate – but the beauty of this approach is that it’s not the only skill they are developing. Sometimes, pupils get the impression that there is only one way to solve a problem. The mastery approach requires each pupil to make a choice. ‘How will YOU solve the problem?’, it asks. The choice a pupil makes is crucial to understanding both how he or she has reached an answer and the thought process that underlies it. Not only does it allow teachers to gain an understanding of the way a pupil’s mind is working and how <span>her</span> thinking process is developing, it is also crucial to correcting misconceptions and instilling deeper understanding in the future.</span></span></span></span></span></p>
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<p>The mastery approach requires each pupil to make a choice. ‘How will YOU solve the problem?’, it asks.</p>
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<p><span><span><span><span><span>Emphasising choice also has another benefit: it encourages pupils to share and compare alternative solutions. As they examine the different ways a problem can be solved, pupils begin to engage in discussions about why one approach may be more efficient than another. This discussion, in turn, leads to a clearer sense of what their preferred method is and how to make a case for it in the classroom. This process of discovery builds both confidence and resilience, essential characteristics pupils will need to help them think clearly and make good decisions when they get stuck. </span></span></span></span></span></p>
<p><span><span><span><span><span>Another key advantage of this sort of problem is that it puts the emphasis on process. In old-style mathematics, it often seemed that nothing mattered but the right answer. By foregrounding choice and discussion, our aim is to show that the process of thinking the problem through is where the real learning takes place, laying the foundations for children to understand things better in the future.</span></span></span></span></span></p>
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<p>Our aim is to show that the process of thinking the problem through is where the real learning takes place, laying the foundations for children to understand things better</p>
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<p><span><span><span><span><span>It’s also important to point out that in Maths Mastery getting the answer correct doesn’t mark the end of the process. Assuming a pupil has (correctly) provided the answer £107 to the problem, then a follow up question – which might look like the one below – marks the final step. </span></span></span></span></span></p>
<p><strong><em>Is £107 a lot of money?</em></strong></p>
<p>So, to the question: ‘Is £107 a lot of money?’, the answer I most like to hear is: ‘It depends...'. <span><span><span><span><span>This second question plays a huge role in helping us determine the number sense a pupil really has. The truth, after all, is that £107 does not have a finite value and its meaning is actually open to interpretation. Far too often in the past, mathematics has been treated as having only a single correct answer. Questions like these allow pupils to reconsider the meaning of the number, developing their understanding in a real-world context.</span></span></span></span></span></p>
<p><span><span><span><span><span>It depends how good a friend Olivia is buying the gift for.</span></span></span></span></span></p>
<p><span><span><span><span><span>It depends how old Olivia and her friends are.</span></span></span></span></span></p>
<p><span><span><span><span><span>It depends whether or not Mr Rodricks needs the money for something else (as Olivia will be asking him for the money).</span></span></span></span></span></p>
<p><span><span><span><span><span>In other words, I like ‘It depends’ because it tells me that pupils are developing an insight into what the number actually means. It tells me what a pupil thinks the true value of £107 is. It tells me that my pupils understand that number value is actually relational and not fixed, which means their understanding of number is growing deeper.</span></span></span></span></span></p>
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<p><span><span><span><span><span>A lot has changed about the way I teach mathematics since I first floated the ‘Eleven Cuppas’ problem all those years ago. Even so, I haven’t entirely consigned it to history. I often tell pupils that it is okay to make mistakes because we learn from them and that applies to me as much as to them. Now I still use the question, but now with a different spin. I no longer view it as a good way to examine patterns. Instead, I treat it as what it is, an excellent way to see if pupils can relate numbers to the real world. And today, it worries me if a student doesn’t ask if I really do drink that much tea.</span></span></span></span></span></p>
<p><em><strong><span><span><span><span><span>Comments and feedback on this blog are welcome to: <a href="mailto:website@harrodian.com">website@harrodian.com</a></span></span></span></span></span></strong></em></p>
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<p>I no longer view 'Eleven Cuppas' as a good way to examine patterns. Instead, I treat it as what it is, an excellent way to see if pupils can relate numbers to the real world.</p>
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Mon, 14 Oct 2019 14:11:20 +0000Warren Rodricks1228 at https://www.harrodian.comMaths Mastery: Why Mastery Matters
https://www.harrodian.com/blog/maths-mastery-why-mastery-matters
<span class="field field--name-title field--type-string field--label-hidden">Maths Mastery: Why Mastery Matters</span>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://www.harrodian.com/user/855" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Warren Rodricks</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Wed, 18/09/2019 - 08:55</span>
<div class="field field--name-field-blog-image field--type-image field--label-hidden field__item"> <img src="https://www.harrodian.com/sites/default/files/blog/2019-09/059_Harrodian_19.jpg" width="960" height="938" alt="Mr Rodricks" typeof="foaf:Image" /></div>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><strong><span><span><span><span><span>In the first installment of his Maths Mastery blog, Mr Rodricks, Head of Junior Prep Mathematics, <em>above</em>, explains what Mastery means and why it matters so much.</span></span></span></span></span></strong></p>
<p><span><span><span><span><span>As I was pondering the best way to start this new Harrodian blog about Maths Mastery in my living room last week, my 12-year old daughter burst in after a day’s shopping, eager to model the new clothes she and her mum had bought. What really excited her about her purchases were their vibrant neon shades of green, yellow and pink. The electric colours struck a nostalgic chord with me, sparking fond memories of my own nineties childhood when I happily sported neon creations all the time rather than just occasionally, as I do today (<em>bottom</em>). But when I tried to explain the idea of retro-influenced fashion cycles to my daughter she was having none of it. ‘No, Daddy,’ she insisted. ‘These are new colours.’ It wasn’t until I provided her with real (and somewhat embarrassing) photographic evidence of my nineties neon fixation that she began to soften her stance. </span></span></span></span></span></p>
<p><span><span><span><span><span>It struck me then that, oddly, the Maths Mastery we are engaged in at Harrodian has something in common with the neon fashion revival my daughter is relishing. Maths Mastery is a distinct way of seeing the world mathematically which is rapidly gaining popularity not just across the United Kingdom but worldwide. It is often described as a new phenomenon and tends to be covered as such in the media. </span></span></span></span></span></p>
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<p>Maths Mastery is often described as a new phenomenon but as with the revival of neon, its roots are firmly grounded in the past</p>
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<p><span><span><span><span><span>As with neon, though, Mastery's roots are firmly grounded in the past: way back in the 1980s, in fact. It was then that the Cockcroft Report, published in the UK, and An Agenda for Action in the USA, both called for a re-think of how mathematics should be taught. The research suggested that in the development of a mathematics system, a focus on calculation tended to limit learners. The report argued that, instead, Mathematics should put problem solving at the centre of its universe, ensuring children of all ages would grow and develop to their full potential. From this seed, Maths Mastery has blossomed into the flourishing movement we are working with today. </span></span></span></span></span></p>
<p><span><span><span><span><span>My own first exposure to Mastery came neither in the UK or the USA but whilst I was teaching overseas in Bangkok. It was my serendipitous presence at a workshop run by a group of Australian teachers which first started me down the Mastery path. This first, thought-provoking day-long session prompted me to do some serious thinking and research of my own. As I observed other mathematics teachers working and searched sources around the world, I began to gather the ingredients of teaching that I knew I wanted to create for my students. Many of the ideas I adopted were drawn from the early years curriculum of the United Kingdom. To this day, when I try to explain the approach, I still find one of the best definitions of Maths Mastery is that it takes the methods of early years teaching and applies them to older children. More examples of what I mean by this and the way it works will follow in forthcoming posts.</span></span></span></span></span></p>
<p><span><span><span><span><span>Today, there are two distinct streams of Mastery teaching out there, one originating from Singapore, the other from Shanghai. After training in both, I’ve discovered that their paths to Mastery are quite distinct. The staff involved, the way a lesson starts and the way ideas are communicated are not the same at all. For me this is where the beauty of the approach lies. Mastery is not a scheme. There is no specific guide that details what each and every lesson should look like and there is certainly no requirement that each lesson should look the same as the last. Nor is there any expectation that two teachers with different classes will produce an exactly similar lesson for their students. </span></span></span></span></span></p>
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<p>Mastery is not a scheme. There is no guide that details what each lesson should look like and there is no requirement that each lesson should look the same as the last.</p>
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<p><span><span><span><span><span>What the two methods do share in common is their sense that studying Mathematics has a wider relevance and a deeper purpose.</span></span></span> <span><span><span>Mastery is grounded in a belief that a world that is fundamentally mathematical in nature requires a language that can reveal its true beauty. Ultimately after all, studying maths means more than just passing a test, it’s about understanding where humanity began, where we are now and what possible future we may have. You know, the little things in life!</span></span></span></span></span></p>
<p><span><span><span><span><span>To parents new to Mastery such ambitions may sound rather grand for children setting out on the maths path at Prep level. I suspect that throughout history every generation of parents has been sceptical about the way their children are taught maths. Mathematics is constantly evolving and, while the changes may seem incredibly exciting for Mathematics specialists, it's only natural that parents are suspicious of an unfamiliar approach which, initially at least, probably sounds dangerously different to what we experienced at school and which initially at least, seems hard to grasp.</span></span></span></span></span></p>
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<p>Mastery is grounded in a belief that studying maths is about understanding where humanity began, where we are now and what future we may have.</p>
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<p><span><span><span><span><span>That’s why, as we continue to hone our approach to Maths Mastery at the Harrodian, talking and discussing the subject becomes more important than ever. It’s vital that our community of pupils and parents knows why we are travelling down this path and how partnership between home and school could look in the future. That is in large part why I wanted to start this blog. What will follow in future entries is a range of insights and explanations of the way Mastery can work at various levels and useful advice about the best way of support pupils with their Mathematics at school and at home. I hope you find it helpful, useful and enlightening. I'd love to know what you think so please feel free to send your comments to me at the address below. Looking forward to hearing from you.</span></span></span></span></span></p>
<p><em>Feedback on this blog is welcome to: <a href="mailto:website@harrodian.com">website@harrodian.com</a></em><br /><br /><img alt="Neon%20Warren.jpg" data-entity-type="" data-entity-uuid="" src="https://www.harrodian.com/sites/default/files/Harrodian%20Images/DoE/NEW%20DoE%20photo%20folder%20Sep%202019/DoE%202019/Gold/Neon%20Warren.jpg" /><br /><br /><br /><br />
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Wed, 18 Sep 2019 07:55:09 +0000Warren Rodricks1184 at https://www.harrodian.com